On the Equivalence of Weak- and Cyclic-Monotonicity

Abstract

We provide an approach to studying the equivalence of weak- and cyclic-monotonicity conditions in convex and non-convex domains with a finite set of outcomes. Using this approach, we establish the new equivalence results for gross-substitutes preferences and single-peaked preferences on posets. We also provide novel applications of the equivalence result to problems in mechanism design, spatial allocation, revealed preference theory, and producer choice theory.

Keywords: weak-monotonicity, cyclic-monotonicity, non-convex domain, mechanism design, spatial allocation, revealed preference theory, producer choice theory, algebraic topology, homology

JEL Classification: D11, D21, D82